Exploring Mathematical Extrapolation of Large Language Models with Synthetic Data

• URL: http://arxiv.org/abs/2406.02100v1
• Date: Tue, 4 Jun 2024 08:30:37 GMT
• Title: Exploring Mathematical Extrapolation of Large Language Models with Synthetic Data
• Abstract summary: We show that the model can perform well on multi-step reasoning tasks via fine-tuning on high-quality synthetic data. Experimental results with the open-llama-3B model on three different test datasets show that the model can reach a zero-shot pass@1 at 0.44.
• Score: 7.52830790706506
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Large Language Models (LLMs) have shown excellent performance in language understanding, text generation, code synthesis, and many other tasks, while they still struggle in complex multi-step reasoning problems, such as mathematical reasoning. In this paper, through a newly proposed arithmetical puzzle problem, we show that the model can perform well on multi-step reasoning tasks via fine-tuning on high-quality synthetic data. Experimental results with the open-llama-3B model on three different test datasets show that not only the model can reach a zero-shot pass@1 at 0.44 on the in-domain dataset, it also demonstrates certain generalization capabilities on the out-of-domain datasets. Specifically, this paper has designed two out-of-domain datasets in the form of extending the numerical range and the composing components of the arithmetical puzzle problem separately. The fine-tuned models have shown encouraging performance on these two far more difficult tasks with the zero-shot pass@1 at 0.33 and 0.35, respectively.

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